In the experiments, we closely follow the evaluation procedure from [1]}. The baseline PINN is a multi-layer perceptron with five hidden layers with 50 neurons and the tanh activation in each hidden layer. Our ensemble of PINNs contains five such networks. The models are trained with the Adam optimizer [2]} with learning rate of 0.001. The two inputs \(x\)  and \(t\)  of the network are normalized to \([-1, 1]\) . Set \(D_\text{L}\)  contains 256 points that define the initial conditions, these points are selected from a regular grid on \(x \in [0, 2\pi ]\)  with \(t=0\) . Set \(I_\text{B}\)  contains 100 points which are selected on a regular grid \(t \in [0, 1]\) . The points for set \(I_\text{PDE}\)  are randomly sampled from a regular grid from the interval \(x \in [0, 2\pi ], t \in [0, 1]\) , in all experiments we sample 1000 points.
For the proposed ensemble method, we use the following hyperparameters: \(\sigma ^2 = 0.0004\) , \(\epsilon =0.001\) , \(\Delta = 0.05\)  and \(\Delta _\text{PDE}=0.1\) .
We perform \(N=1000\)  gradient updates before extending sets \(I_\text{PL}^{\prime }\) , \(I_\text{PDE}^{\prime }\) , \(I_\text{B}\) , except for the first update that is applied after \(N=5000\)  training steps. A greater number of iterations is required before the first update since the network is initially untrained.
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